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Symbolic Regression Is All You Need: From Simulations to Scaling Laws in Binary Neutron Star Mergers

P. Darc, Clecio R. Bom, Charles Kilpatrick, Bernardo M. O. Fraga, Gabriel S. M. Teixeira

TL;DR

This work addresses the challenge of linking binary neutron star merger parameters to post-merger disk ejecta in an interpretable way. It applies AI-driven symbolic regression (SR) using PySR and PyOperon to NR simulation data, deriving closed-form expressions for the post-merger disk mass $M_{ m disk}$ that balance accuracy and simplicity, aided by physics-informed templates. The SR-derived models often outperform traditional fits on an independent test set, with some expressions beating the Lund et al. 2025 formula and the ability to use alternative predictor sets such as $(M_1,M_2, ilde{\Lambda})$, enabling new EOS constraints from EM observations. The results demonstrate that SR can yield robust, physically meaningful scaling relations that generalize beyond calibration data, offering a valuable tool for multimessenger astrophysics and neutron star EOS studies.

Abstract

Gravitational wave sources with electromagnetic counterparts have highlighted the need for predictive, interpretable models linking the parameters of compact binary systems to post-merger remnants and mass outflows. In this work, we explore AI-driven symbolic regression (SR) frameworks to derive updated analytical relations for disk ejecta mass in binary neutron star mergers, trained on state-of-the-art numerical relativity simulations. Our method reveals a set of compact equations that outperform existing fitting formulae across multiple statistical metrics while remaining physically interpretable. Notably, SR also enables alternative predictor sets (e.g., $\{M_1,M_2,\tildeΛ\}$) that match or exceed the accuracy of models relying solely on compactness of the lightest neutron star ($C_1$), enabling new parameter constraints from electromagnetic observations. Unlike traditional black-box machine learning models, these closed-form expressions generalize robustly to regions of the parameter space not represented in the training data, offering a physics-informed tool for multimessenger observations and constraints on the neutron star equation of state.

Symbolic Regression Is All You Need: From Simulations to Scaling Laws in Binary Neutron Star Mergers

TL;DR

This work addresses the challenge of linking binary neutron star merger parameters to post-merger disk ejecta in an interpretable way. It applies AI-driven symbolic regression (SR) using PySR and PyOperon to NR simulation data, deriving closed-form expressions for the post-merger disk mass that balance accuracy and simplicity, aided by physics-informed templates. The SR-derived models often outperform traditional fits on an independent test set, with some expressions beating the Lund et al. 2025 formula and the ability to use alternative predictor sets such as , enabling new EOS constraints from EM observations. The results demonstrate that SR can yield robust, physically meaningful scaling relations that generalize beyond calibration data, offering a valuable tool for multimessenger astrophysics and neutron star EOS studies.

Abstract

Gravitational wave sources with electromagnetic counterparts have highlighted the need for predictive, interpretable models linking the parameters of compact binary systems to post-merger remnants and mass outflows. In this work, we explore AI-driven symbolic regression (SR) frameworks to derive updated analytical relations for disk ejecta mass in binary neutron star mergers, trained on state-of-the-art numerical relativity simulations. Our method reveals a set of compact equations that outperform existing fitting formulae across multiple statistical metrics while remaining physically interpretable. Notably, SR also enables alternative predictor sets (e.g., ) that match or exceed the accuracy of models relying solely on compactness of the lightest neutron star (), enabling new parameter constraints from electromagnetic observations. Unlike traditional black-box machine learning models, these closed-form expressions generalize robustly to regions of the parameter space not represented in the training data, offering a physics-informed tool for multimessenger observations and constraints on the neutron star equation of state.

Paper Structure

This paper contains 14 sections, 13 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Symbolic Regression & Numerical Relativity Simulation Dataset
  3. Results
  4. Conclusion
  5. Radice et al. (2018) Radice2018:
  6. Coughlin et al. (2019) Coughlin2019:
  7. Krüger & Foucart (2020) Kruger2020:
  8. Dietrich et al. (2020) Dietrich2020:
  9. Lund et al. (2025) Lund2025:
  10. PySR_Free_Core (Complexity 8):
  11. PySR_Free_Ext (Complexity 9):
  12. PySR_Free_All (Complexity 8):
  13. PySR_Free_M12 (Complexity 13):
  14. PySR_Template_LLM (Complexity 20, simplified to 16):

Figures (1)

  • Figure 1: Predicted disk mass versus disk mass from numerical relativity simulations. The left panel (\ref{['fig:sr_ytrue']}) presents results obtained with symbolic regression expressions, while the right panel (\ref{['fig:lit_ytrue']}) shows results from literature fitting formulae together with the PySR Template expression proposed by the LLM. Purple points correspond to the calibrated regime (Krüger20 dataset), whereas orange points represent the uncalibrated regime (Nedora21 dataset). Each inset box reports the model name, mean absolute error, mean squared error, expression complexity, and coefficient of determination ($R^2$).